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Transcript
Guided Notes for Chapter 4 Lesson 4.1 Triangle Sum Conjecture Triangle Sum Conjecture The sum of the measures of the angles in every triangle is . Third Angle Conjecture If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle is each triangle is equal in measure to the in the other triangle. Lesson 4.2 Properties of Special Triangles In an isosceles triangle, the angle between the two congruent sides is called the angle, and the other two angles are called the base angles. The side between the two base angles is called the of the isosceles triangle. The other two sides are called the . Isosceles Triangle Conjecture If a triangle is isosceles, then its angles are Converse of the Isosceles Triangle Conjecture If a triangle has two angles, then it is an . triangle. Lesson 4.3 Triangle Inequalities Triangle Inequality Conjecture The of the lengths of any two sides of a triangle is the length of the third side. than Side-Angle Inequality Conjecture In a triangle, if one side is longer than another side, then the angle opposite the longer side is than the angle opposite the side. If you extend one side of a triangle beyond its vertex, then you have constructed an at that vertex. Each exterior angle of a triangle has an angle and a pair of angles. The angles are the two angles in the triangle that do not share a vertex with the exterior angle. Triangle Exterior Angle Conjecture The measure of an angle of a triangle is the measures of the angles. the of Lesson 4.4 Are There Congruence Shortcuts? There are different ways that the same three parts of two triangles may be congruent. An angle that is included between two sides of a triangle is called an . A side that is included between two angles of a triangle is called an . SSS Congruence Conjecture If the three sides of one triangle are congruent to the three side of another triangle, then the . SAS Congruent Conjecture If two sides and the included angle of one triangle are congruent to two sides and the angle of another triangle, the triangles are . Lesson 4.5 Are There Other Congruence Shortcuts? ASA Congruence Conjecture If two angles and the side of one triangle are congruent to two angles and the side of another triangle, then the triangles are . SAA Congruence Conjecture If two angles and a side of one triangle are congruent to the angles and side of another triangle, then the triangles are . Lesson 4.6 Corresponding Parts of Congruent Triangles The definition of congruent triangles states that if two triangles are congruent, then the parts of those congruent triangles are congruent. This is referred to as . Lesson 4.7 Flowchart Thinking A is a concept map that shows all the steps in a complicated procedure in proper order. Arrows connect the boxes to show how facts lead to conclusions. To present your reasoning in flowchart form, create a Place each statement in a box. Write the logical reason for each statement beneath its box. Lesson 4.8 Proving Isosceles Triangle Conjecture Vertex Angle Bisector Conjecture In an isosceles triangle, the bisector of the vertex angle is also the and the to the . Equilateral/Equiangular Triangle Conjecture Every triangle is and, conversely, every triangle is equilateral. .